For the probabilty density function `f(x) [ {:(,cx(1-x)^(3),0 lt x lt 1),(,0,"elsewhere"):}` find the constant c.

A random variable X has a probability density function f(x) ={{:(,k,0 lt x lt 2pi),(,0,"elesewhere"):} find (i) k , (ii) P ( 0 lt X lt pi//2) (iii) P(pi//2 lt X lt 3pi//2)

The random variable X has the probability density function f(x)={{:(ax+b, 0 lt x lt 1), (0, "otherwise"):} and E(X)=7/12 , then a and b are respectively

Let X be random variable with probability density function f(x)={{:(2/x^(3), x ge 1), (0, x lt 1):} Which of the following statement is correct

If X is the random variable with porbability density function f(x) given by f(x)={(x-1,1lt=xlt2),(-x+3,2lt=xlt3),(0,"otherwise"):} find (i) the distribution function F(x) (ii) P (1.5lt=X lt=2.5)

The time to failure in thousands of hours of an electronic equipment used in a manufactured computer has the density function f(x)={{:(3e^(-3x), x gt 0), (0, "elsewhere"):} Find the expected life of this electronic equipment.

The probability density function of X is f(x) = {(x,0 ltxlt1),(2-x, 1lt=xlt2),(0,"otherwise"):} Find (i) P(0.2 lt=X lt0.6) (ii) P(1.2lt= X lt 1.8) (iii) P(0.5 lt=X lt 1.5)

The probability density function of X is f(x)={{:(x, 0 lt x lt 1), (2-x, 1 le x lt 2), (0, "otherwise"):} Find P(0.5 le X lt 1.5)

The probability density function of X is f(x)={{:(x, 0 lt x lt 1), (2-x, 1 le x lt 2), (0, "otherwise"):} Find P(0.2 le X lt 0.6)

The probability density function of X is f(x)={{:(x, 0 lt x lt 1), (2-x, 1 le x lt 2), (0, "otherwise"):} Find P(1.2 le X lt 1.8)

Find the mean and variance of the distribution f(x) = {(3e""^(-3x),0lt xltoo),(0,"elsewhere"):}